Question

A 20 yr maturity bond with par value of $1000 makes semi-annual coupon payment at a coupon rate of 8%. What is the effective annual yield if the bond price is $950?

The answer is 8.7%
Please show work, USING THE BA CALCULATOR. Thank you.

Answer 1

Information provided:

Par value= future value= $1,000

Time= 20 years*2= 40 semi-annual period

Coupon rate= 8%/2= 4%

Coupon payment= 0.04*1,000= $40

Current price= present value= $950

The question is solved by first calculating the yield to maturity.

Enter the below in a BA Plus II financial calculator to compute the yield to maturity:

FV= 1,000

N= 40

PMT= 440

PV= -950

The value obtained is 4.2626.

Therefore, the yield to maturity is 4.2626*2= 8.5251%.

The effective annual yield is calculated using the below formula:

Effective annual yield= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

Effective annual yield = ( 1 + 0.0853/2)^2 – 1

                                          = 1.0871 – 1

                                          = 0.0871*100

                                          = 8.7068%8.7%.

In case of any query, kindly comment on the solution.